Inspired by my academic grandfather's Thomas's work on solving a family of cubic Diophantine equations, my coauthors and I explore other families of parametrized Thue equations. We let $t$ be an imaginary quadratic integer and define a family of Thue equations over imaginary quadratic integers with $t$ as a parameter. After a brief introduction, I will present our results on solving such a family of Thue equations. The proof uses methods and techniques that expand upon work by Bennett, Chen and Voutier, Heuberger, Lettl, Peth{\"o}, and Voutier, and Peth{\"o}.